MinT - Best Known (187−51, 187, s)-Nets in Base 4

Best Known (187−51, 187, s)-Nets in Base 4

(187−51, 187, 531)-Net over F₄ — Constructive and digital

Digital (136, 187, 531)-net over F₄, using

t-expansion [i] based on digital (135, 187, 531)-net over F₄, using
- 5 times m-reduction [i] based on digital (135, 192, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 64, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(187−51, 187, 1184)-Net over F₄ — Digital

Digital (136, 187, 1184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−51, 187, 102269)-Net in Base 4 — Upper bound on s

There is no (136, 187, 102270)-net in base 4, because

1 times m-reduction [i] would yield (136, 186, 102270)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9621 668059 393056 500319 142570 253110 412928 543751 537182 225735 674927 092766 590285 022076 021194 475769 570014 238470 236239 > 4¹⁸⁶ [i]